2D electrons under Quantum Hall effect mapped by SPM microscopy and visualized with 3D SPM software

Visualization of the Scanning Probe Microscope (SPM) images using multiple layer 3D SPM software.

Advanced multiple layer visualization provides researcher with many 3D surfaces in one screen for detailed comparison of different samples
or SPM data taken for the same sample under different experimental conditions.

ScienceGL Inc. has developed multiple layer visualization engine that lets the scientist to analyze several microscopy images in one interactive 3D screen. This feature helps researcher to compare changes in sample in real time. We also propose to use interactive 3D measurement tools for reading back essential data details such as intersection plots, volumes and distances in measured data.

Scanning probe microscopy of the electron liquid. The SPM data is taken in scanning capacitive mode. The quantum Hall effect for electrons confined in quantum walls is studied with high resolution SPM technique to reveal physical properties of the 2D confined electrons.
Fig.1. Mapping of the electron liquid under quantum hall effect using 3D SPM data visualization. The resulting topographic electron map is represented as 3D surface in enhanced mode using height coloring and 3D axis for better perception of the electron density in the plane of the sample.
Scanning Probe Microscopy data courtesy Prof. Gleb Finkelstein,  Duke University Physics Department.
Multiple surface visualization approach is used for detailed investigation of the Scanning Probe Microscopy data. Quantum Hall effect is observed for electron gas under 2D confinement conditions. Two-dimensional electron gas density map is measured under different experimental conditions.
Fig.2. 3D visualization of two SPM images for comparison of electron densities under different experimental conditions. SPM data courtesy Prof. Gleb Finkelstein. 3D mapping of the effect results in double surfaces that are enhanced with different color palettes for better perception of the features under investigation.

Fig.3. Two SPM images of the 2D confined electron gas measured in scanning capacitive mode are visualized as 3D surfaces for comparison of the data taken under different experimental conditions. The intersection cut tool is used to read out 1D profiles for detailed comparison of the electron densities.

The images above correspond to of electrons as they move within a nearly two-dimensional (flat) structure made of Ga, As, and Al atoms. In nature, most electrons exist as parts of atoms; in this image, they are flowing free in a low-temperature electron gas. A strong magnetic field created the flowing pattern, a result of the quantum Hall effect. A scanned probe microscope, a research tool that can observe and manipulate objects down to the scale of a single atom, took the images.

Prof. Gleb Finkelstein publication:
Topographic Mapping of the Quantum Hall Liquid Using a Few-Electron Bubble
G. Finkelstein, 1 P. I. Glicofridis, 1 R. C. Ashoori, 1 M. Shayegan 2 , Science 289, 90-94. (2000).

A scanning probe technique was used to obtain a high-resolution map of the random electrostatic potential inside the quantum Hall liquid. A sharp metal tip, scanned above a semiconductor surface, sensed charges in an embedded two-dimensional (2D) electron gas. Under quantum Hall effect conditions, applying a positive voltage to the tip locally enhanced the 2D electron density and created a "bubble" of electrons in an otherwise unoccupied Landau level. As the tip scanned along the sample surface, the bubble followed underneath. The tip sensed the motions of single electrons entering or leaving the bubble in response to changes in the local 2D electrostatic potential.

Prof. Gleb Finkelstein report at the ITP, UCSB:
Single-Electron Topography of the Quantum Hall Liquid Using a Mobile Quantum Dot
Gleb Finkelstein, MIT

While scanning a sharp metal tip just above the surface of a semiconductor we sense the motion of single electrons within a two-dimensional electron gas buried about 100 nm below. We use the scanning tip to create an electron droplet by locally "gating" the electron gas to accumulate electrons. In the quantum Hall regime an incompressible strip with integer filling surrounds the droplet and leads to a charge quantization. We move the tip across the sample and drag the resulting quantum dot underneath the tip. We monitor the the Coulomb blockade pattern as single electrons enter or leave the quantum dot according to the changes in the local electrostatic potential. This allows us to measure the random electrostatic potential directly as it is seen by the electrons inside the semiconductor.

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